Abstract
LetR denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. ClassR is striclty larger than the class of Valdivia compact spaces. We show that every compact connected Abelian group which is a topological retract of a space from classR is necessarily isomorphic to a product of metric compacta. This completes the result of Uspenskij and the author, where a compact Abelian group outside classR has been described.
Resumen
SeaR la clase mínima de espacios compactos que contiene a todos los espacios compactos métricos y que es cerrada para la operación de tomar límites de sucesiones continuas inversas de retracciones. La claseR es estrictamente mayor que la clase de los espacios compactos de Valdivia. Demostramos que todo grupo abeliano compacto conexo que es un retracto topológico de un espacio de la claseR es necesariamente isomorfo al producto de espacios métricos compactos. Este resultado completa el de Uspenskij y el autor, en el que se describe un grupo compacto abeliano que no pertenece a la claseR.
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Kubiś, W. Valdivia compact Abelian groups. Rev. R. Acad. Cien. Serie A. Mat. 102, 193–197 (2008). https://doi.org/10.1007/BF03191818
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DOI: https://doi.org/10.1007/BF03191818